4 Zero-Crossings as an Edge Detector Raw zero-crossings (no contrast thresholding) Zero-Crossings as an Edge Detector Raw zero-crossings (no contrast thresholding) LoG sigma =, zero-crossing LoG sigma = 4, zero-crossing Zero-Crossings as an Edge Detector Raw zero-crossings (no contrast thresholding) Note: Closed Contours You may have noticed that zero-crossings form closed contours. It is easy to see why Think of equal-elevation contours on a topo map. Each is a closed contour. Zero-crossings are contours at elevation = 0. LoG sigma = 8, zero-crossing remember that in our case, the height map is of a LoG filtered image - a surface with both positive and negative elevations Other uses of LoG: Blob Detection Pause to Think for a Moment: How can an edge finder also be used to find blobs in an image? Lindeberg: ``Feature detection with automatic scale selection''. International Journal of Computer Vision, vol 30, number, pp ,

6 Key idea: Cross correlation with a filter can be viewed as comparing a little picture of what you want to find against all local regions in the image. Efficient Implementation Approimating LoG with DoG LoG can be approimate by a Difference of two Gaussians (DoG) at different scales Maimum response: dark blob on light background Minimum response: light blob on dark background Maimum response: vertical edge; lighter on left Minimum response: vertical edge; lighter on right D eample M.Hebert, CMU Efficient Implementation Back to Blob Detection LoG can be approimate by a Difference of two Gaussians (DoG) at different scales. Separability of and cascadability of Gaussians applies to the DoG, so we can achieve efficient implementation of the LoG operator. DoG appro also eplains bandpass filtering of LoG (think about it. Hint: Gaussian is a low-pass filter) Lindeberg: blobs are detected as local etrema in space and scale, within the LoG (or DoG) scale-space volume. Other uses of LoG: Blob Detection Other uses for LOG: Image Coding Coarse layer of the Gaussian pyramid predicts the appearance of the net finer layer. The prediction is not eact, but means that it is not necessary to store all of the net fine scale layer. Laplacian pyramid stores the difference. Gesture recognition for the ultimate couch potato 6

7 Other uses for LOG: Image Coding takes less bits to store compressed versions of these than to compress the original full-res greyscale image The Laplacian Pyramid as a Compact Image Code Burt, P., and Adelson, E. H., IEEE Transactions on Communication, COM-3: (983). 7

Lecture 31: Object Recognition: SIFT Keys Motivation Want to recognize a known objects from unknown viewpoints. find them in an image database of models Local Feature based Approaches Represent appearance

Edge detection (Trucco, Chapt 4 AND Jain et al., Chapt 5) Definition of edges -Edges are significant local changes of intensity in an image. -Edges typically occur on the boundary between two different

BIL 719 - Computer Vision Mar 5, 2014 Image pyramids Aykut Erdem Dept. of Computer Engineering Hacettepe University Image Scaling This image is too big to fit on the screen. How can we reduce it? How to

image processing images images: what are they? what is shown in this image? What is this? what is an image images describe the evolution of physical variables (intensity, color, reflectance, condutivity)

Canny Edge Detection 09gr820 March 23, 2009 1 Introduction The purpose of edge detection in general is to significantly reduce the amount of data in an image, while preserving the structural properties

Vision based Vehicle Tracking using a high angle camera Raúl Ignacio Ramos García Dule Shu gramos@clemson.edu dshu@clemson.edu Abstract A vehicle tracking and grouping algorithm is presented in this work

Global and Local Etrema Using the power of calculus, we can draw quite accurate sketches of a given function using a limited amount of information. In order to graph, and reason visually about functions,

Image Enhancement: Frequency domain methods The concept of filtering is easier to visualize in the frequency domain. Therefore, enhancement of image f ( m, n) can be done in the frequency domain, based

Optical Flow as a property of moving objects used for their registration Wolfgang Schulz Computer Vision Course Project York University Email:wschulz@cs.yorku.ca 1. Introduction A soccer game is a real

296 (6 20) Chapter 6 Factoring 6.4 FACTORING a 2 b c WITH a 1 In this section The ac Method Trial and Error Factoring Completely In Section 6.3 we factored trinomials with a leading coefficient of 1. In

4.3 CONNECTING f ' AND f '' WITH THE GRAPH OF f First Derivative Test for Etrema We have alread determined that relative etrema occur at critical points. The behavior of the first derivative before and

Ground Rules PC11 Fundamentals of Physics I Lectures 3 and 4 Motion in One Dimension Dr Tay Seng Chuan 1 Switch off your handphone and pager Switch off your laptop computer and keep it No talking while

Color Image Processing What is color? Selective emission/reflectance of different wavelengths What is color? Illumination Reflectance What is color stimuli? X Illumination Reflectance What is perceived

1 of 10 1/25/2008 3:38 AM SIGNAL PROCESSING & SIMULATION NEWSLETTER Note: This is not a particularly interesting topic for anyone other than those who ar e involved in simulation. So if you have difficulty

CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average

Lecture 1-10: Spectrograms Overview 1. Spectra of dynamic signals: like many real world signals, speech changes in quality with time. But so far the only spectral analysis we have performed has assumed

Physics 101 Prof. Ekey Chapter 5 Force and motion (Newton, vectors and causing commotion) Goal of chapter 5 is to establish a connection between force and motion This should feel like chapter 1 Questions

International Journal of Electronic and Electrical Engineering. ISSN 0974-2174, Volume 7, Number 5 (2014), pp. 505-510 International Research Publication House http://www.irphouse.com Real Time Traffic

EP5 Note No. 7 Wave Interference and Di raction 7.1 Superposition of Two Waves of Equal Wavelength When two waves of equal amplitude and wavelength, but with a phase di erence are superposed, E 0 sin(k!t)

Chapter 5 STRESS TRANSFORMATION AND MOHR S CIRCLE 5.1 Stress Transformations and Mohr s Circle We have now shown that, in the absence of bod moments, there are si components of the stress tensor at a material

A Multiresolution Spline With Application to Image Mosaics PETER J. BURT and EDWARD H. ADELSON RCA David Sarnoff Research Center We define a multiresolution spline technique for combining two or more images

in Acceleration Measurement Systems February 2013 By: Bruce Lent Topics to discuss Definition of dynamic range The effective range Making full use of the high level Using filters to improve dynamic range

Haris Papasaika-Hanusch Institute of Geodesy and Photogrammetry, ETH Zurich haris@geod.baug.ethz.ch Images and Digital Images A digital image differs from a photo in that the values are all discrete. Usually

Color to Grayscale Conversion with Chrominance Contrast Yuting Ye University of Virginia Figure 1: The sun in Monet s Impression Sunrise has similar luminance as the sky. It can hardly be seen when the

Heimadæmi 2 Due: 11:00pm on Thursday, January 28, 2016 You will receive no credit for items you complete after the assignment is due. Grading Policy Exercise 21.56 The dipole moment of the water molecule

Section V.: Magnitudes, Directions, and Components of Vectors Vectors in the plane If we graph a vector in the coordinate plane instead of just a grid, there are a few things to note. Firstl, directions

Lesson 6 Applications of Differential Calculus The line tangent to the graph of a function f at ( 0, f ( 0 is the line passing through the point whose slope is f ( 0. y = f ( The slope-point equation of

Introduction to Fourier Series We ve seen one eample so far of series of functions. The Taylor Series of a function is a series of polynomials and can be used to approimate a function at a point. Another

MA9-A Applied Calculus for Business 006 Fall Homework 8 Solutions Due 0/7/006 0:0AM. # Find the interval(s) where the function f () = + + is increasing and the interval(s) where it is decreasing. First,

REALISTIC CAST SHADOW EFFECT Photoshop s Drop Shadow layer style may be great for adding simple shadows to images or text, making them look as if they re floating slightly above their background, but when

MATH - Area Between Curves Philippe Laval September, 8 Abstract This handout discusses techniques used to nd the area of regions which lie between two curves. Area Between Curves. Theor Given two functions

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage

Written by Jonathan Sachs Copyright 1996-1999 Digital Light & Color Introduction A scanner is a device that converts images to a digital file you can use with your computer. There are many different types